Development and validation of a rating curve for the Ganga River at the Varanasi bend

The most important basic technique to determine discharge in an open channel flow (like a river) is to measure the gauge followed by the calculation of discharge using an empirically generated gauge discharge rating curve (Abhash et al. 2023). This oldest approach has been in practice since 1890 to gauge the Rio Grand at Embudo, New Mexico. The creation of an empirical rating curve for a river involves the joint assessment of gauge and discharge measurements. Flow velocity is directly measured at multiple vertical positions beneath the water surface across various subsections of the channel. The measurements are conducted using either current metres (Rantz 1982) or more modern techniques like acoustic Doppler current profilers (Zhou et al. 1994). Discharge for a specific section is determined by summing the products of subsection areas and their corresponding estimated average velocities (Rantz 1982; Naeimi et al. 2019). Although this approach is known for its accuracy, it has some limitations. First, direct flow velocity measurements are very difficult or impossible during floods with the help of current metres or ADCPs (Chauhan et al. 2014). Second, the development and maintenance of the rating curve of any river is quite expensive and difficult due to the need for very huge skilled manpower (Medisetty et al. 2020; Srivastava et al. 2023). Third, for measurement convenience and safety, gauge sites are often located at geographically difficult sites, which include bridges, narrow sections suitable for cableways, and wide sections suitable for wading (Ahmadi et al. 2020). Due to the characteristics of these sites, they often are vulnerable to erosion and deposition, which requires extra flow measurements to define stage-dependent or post-flood shifts to the rating curves (Omar et al. 2021). Newly developed techniques for computing velocity and shear stress fields in streams and rivers, particularly for sediment transport and geomorphic applications, offer potential solutions to address certain challenges in the existing methods (Gaur et al. 2023). In the last few decades, efforts have been made to improve conventional gauging methods. The improved methods emphasized developing techniques to measure gauge and discharge remotely. The advantage of these techniques is that there is no loss of human life and no damage to measuring instruments.

It is worth noting that surface velocity measurements obtained remotely from the river's edge using Doppler radar have been utilized to estimate discharge at a specific cross-section (Gupta et al. 2022a). In this approach, a ground-penetrating radar, suspended from a cableway, is employed for the remote measurement of cross-sectional geometry (Spicer et al. 1997; Costa et al. 2000; Cheng et al. 2004; Chauhan et al. 2013). However, this method involves expensive equipment and is particularly well-suited for measuring discharge in channels with unstable beds. Another alternative involves surface velocities measured remotely through video cameras and particle image velocimetry algorithms, which have been successfully employed for discharge determination (Bradley et al. 2002; Creutin et al. 2003). The advantage of this technique lies in its relative cost-effectiveness and portability. Nevertheless, it requires clearly identifiable tracers in the flow. If such tracers are not naturally present in the form of foam or floating debris, they must be introduced artificially (Shekhar et al. 2021). Additionally, similar to the Doppler radar method, the determination of cross-sectional geometry must be conducted independently. It is widely recognized that currently available streamflow routing packages, such as Hydrologic Engineering Center-River Analysis System (HEC–RAS) (U.S. Army Corps of Engineers 2002; User's manual ‘HEC-RAS’ 2010), may not be suitable for achieving the goal of extending or developing a rating curve at a site under the mentioned circumstances. This limitation arises from their demanding requirements for detailed channel cross-section information and roughness data at close intervals. However, approximate flood routing techniques could prove more effective for this purpose, given their ability to handle sparse spatial details (Chauhan et al. 2015). Considering that the rating curve sites seeking extension or development are typically situated on mainstreams, the chosen approximate routing technique should also be capable of routing flows in compound channels, which include both a main channel and an adjoining floodplain channel (Gupta et al. 2022b). This type of investigation requires a deep knowledge of the work related to the topic of concern.

The main aim of this study is to measure the flow properties of the Ganga River at Varanasi bend using the latest technology (ADCP) and to generate the rating curve for the Ganga River with the measured flow properties of the river. For this, 14 cross-sections of the Ganga from Ramnagar (upstream) to Rajghat (downstream) have been identified and prepared.

This research focuses on addressing the limitations of traditional gauge-discharge measurement methods during flood conditions, particularly at the Varanasi bend of the River Ganga. By incorporating ADCP and innovative remote-sensing techniques, this study establishes a robust stage–discharge relationship tailored to dynamic and challenging environments. Unlike the existing literature, which often struggles with evolving stream channels and extreme hydrological events, this work proposes and validates a novel rating curve equation, providing a reliable tool for real-time discharge prediction. The study's emphasis on continuous monitoring and adaptability ensures practical utility for river management and hydrological modelling.

The study area, Varanasi (25° 20′ N and 83° 07′ E), is situated in the middle Ganga valley of North India, specifically in the eastern part of the state of Uttar Pradesh. The left crescent-shaped bank of the Ganga at Varanasi spans an average elevation between 50 feet (15 m) and 70 feet (21 m) above the river (Mohanty 1993). Varanasi is renowned as the oldest city located on the convex bank of the holy River Ganga, considered the longest river in India with a total length of 2,525 km from Gangotri to Ganga Sagar. The ‘Varanasi Urban Agglomeration’ comprising seven urban sub-units covers an area of 112.26 km². Being positioned in the Indo-Gangetic Plains of North India, the region benefits from fertile land due to regular low-level floods in the Ganga, which continually replenish the soil (Singh et al. 2023). Varanasi is often described as being located between two confluences: one of the Ganga and Varuna and the other of the Ganga and Assi. However, it 's important to note that the latter is more accurately characterized as a rivulet rather than a full-fledged river. The distance between these two confluences is approximately 4.0 km. A notable religious practice for Hindus is the Pancha-kroshi Yatra, a round trip covering 8.3 km between these two places, culminating in a visit to a Sakshi Vinayak Temple, considered a sacred ritual.

The climate in Varanasi, reflective of Northern India in general, is tropical in nature, featuring extremes of temperature. Winter temperatures can drop to a minimum of 3°C, while summer temperatures can soar to a maximum of 47°C. The annual rainfall in the region ranges from 680 to 1,500 mm, with a significant portion occurring during the monsoon season, typically spanning from July to September.

The city's topography is predominantly flat with a gentle slope towards the River Ganga. Varanasi is situated on the northern bank of the river, characterized by an elevated terrain that prevents flooding in most areas. The region is part of the Indo-Gangetic Plain, with an altitude ranging from 70 to 80 m above sea level. Notable features include natural levees and riverine terraces, contributing to its unique landscape. The topography supports urban development and agriculture while influencing drainage patterns and water resource management. Varanasi primarily features alluvial soil, formed by the deposition of sediments from the River Ganga and its tributaries. The soil is fertile, with a high concentration of clay, silt, and fine sand, making it suitable for agriculture. The pH levels range from neutral to slightly alkaline, with moderate organic content. The soil exhibits good water retention but can be prone to waterlogging in low-lying areas.

In this study, a rating curve is developed for the river gauge at the M-1 cross-section with the help of data collected from November 2012 to March 2013, which is obtained with the help of ADCP and is validated with the help of the remaining 28 days of data taken during the same time of cross-section investigation. For the generation of the rating curve for the river gauge, the M-1 profile is selected as a suitable cross-section. It is located downstream at Rajghat Bridge, Varanasi (India).

As previously discussed, the direct method of measuring discharge entails a two-step process. The initial step of paramount significance involves establishing the stage–discharge relationship (G–Q). Once this relationship is determined, the subsequent step is to measure the stage (G) in order to obtain the corresponding discharge (Q) using the established (G–Q) relationship. The latter part of this process is considered a routine operation. Ultimately, the objective of all direct-discharge measurements, including those with current meters, is to establish a stage–discharge relationship for the specific channel gauging section. This relationship, commonly known as the rating curve, is crucial for hydrological analysis. The plotted values of measured discharge against the corresponding stage provide a representation that integrates the influence of various channels and flow parameters. This integrated effect is termed ‘control.’ If the (G–Q) relationship for a gauging section remains constant and does not undergo changes over time, it is described as having permanent control. However, if the relationship changes with time, it is referred to as shifting control.

In plots (arithmetic or logarithmic), discharge is plotted in the abscissa, and gauge height or stage is plotted, as the ordinate. Discharge measurements are numbered sequentially in chronological order to facilitate the identification of time trends. Significant exercise is done based on various factors such as knowledge of the river and the quality and magnitude of each measurement to consider the best curve.

In this context, the variable ‘r’ indicates the degree of linearity between the two sets of data. A perfect correlation is denoted by ‘r = 1.0.’ A correlation between 0.6 and 1.0 is generally considered good. It is important to highlight that, in the current scenario, where discharge Q increases with (G − a), the variables Y and X are positively correlated, resulting in a positive value for ‘r.’

For the development of the rating curve of the River Ganga at the M-1 cross-section, the continuous measurement of the cross-section is done with the help of ADCP and auto level from November 2012 to March 2013. The water level at the cross-section was measured thrice a day, i.e. at 8.00 A.M., 01.00 P.M., and 6.00 P.M., with the help of an auto-level continuously. For the development of the rating curve, the gauge data have been taken as the average of the readings taken in the whole day for improvement of the rating curve equation. Another measurement for the discharge data ADCP was used at the cross-section M-1. For the measurement of discharge at the cross-section, the whole cross-section is marked with the help of a total station at both ends of the river. After the marking of the points at both ends, a motorboat at which the ADCP was mounted with the recording laptop connected with the ADCP was used for the measurement of discharge, and this process was repeated for the measurement of discharge at the M-1 section of the River Ganga. The calculation of ‘a’ (gauge height at zero discharge theoretically) is done with the help of the method discussed in step 3 in the section of calculation of stage for zero discharge (theoretically) (Subramanya 2009).

The validation of the rating curve was generated for the River Ganga with the help of the remaining 28 data of discharge and gauge height, respectively. These data are randomly selected from the complete data of 86 days from the measurement of 5 months, from November 2012 to March 2013. The percentage error obtained from the equation is a maximum of 11.74% and a minimum of 0.0351%, as shown in Table 3. It is observed that only about 10% error is obtained in the development of the rating curve. Although the entire data collection work is done by electronic measurements, the cross-section of such a large river is very complex and irregular and accurate measurement of this cross-section is a challenge. Hence, this error of 10% is acceptable.

The development of the rating curve for the Ganga River at the Varanasi bend aims to illustrate the correlation between stage and discharge at the M-1 cross-section. Rating curves typically exhibit a breakpoint, often occurring at the stage where the river overflows its banks or at a lower stage if there is a significant alteration in the riverbed cross-section. Beyond this stage, the river's rise is less rapid, assuming other factors remain constant. Continuous measurement of the river's discharge is impractical. However, the discharge can be determined by applying the stage–discharge relation, commonly known as the rating. These relations are established for stream gauges by physically measuring the river's flow using a mechanical current metre or an ADCP at various stages. Each discharge measurement corresponds to a stage measurement, as illustrated in Tables 2 and 3. Additionally, these relations require constant scrutiny against ongoing discharge measurements due to the dynamic nature of stream channels. Changes in stream channels, such as erosion, deposition of streambed materials, seasonal vegetation growth, debris, or ice, can impact these relations. New discharge measurements plotted on an existing stage–discharge relation graph help identify these changes, allowing adjustments to the rating for accurate discharge estimation at measured stages.

• 1. The rating curve equation is developed from the measured discharge and gauge data of the river at cross-section M-1 by ADCP, where gauge height is taken at the X-axis and the discharge measurement is taken at the Y-axis, respectively. The developed rating curve equation is given in the following:

  

• 2. The developed equation is validated for the measured data of 28 days, and the result is given in Table 2. Table 3 indicates that the discharge values derived from the rating curve equation align closely with the measured discharge data, showcasing a maximum error within the acceptable range of ±10%. This level of deviation falls within the acceptable limits for the equation, particularly considering the inherent challenges in accurately measuring discharge during flood conditions in the Ganga River at Varanasi.

• 3. The suggested rating curve equation proves beneficial for estimating the discharge of the Ganga River at Varanasi, particularly in flood conditions. In such scenarios, with the gauge height obtained, the proposed equation enables an effective estimation of the river's discharge.

The research undertaken to develop and validate a rating curve for the River Ganga at the Varanasi bend, specifically at the M-1 cross-section, has yielded valuable insights into discharge estimation in an open channel flow. The study emphasized the importance of accurate and reliable discharge measurements, acknowledging the challenges associated with traditional methods, especially during flood conditions.

The adoption of advanced techniques, such as the use of ADCP, provided a more robust and remote approach to gauge and discharge measurements. The developed rating curve equation has shown significant promise in accurately estimating river discharge based on gauge height. The validation process, conducted with a set of 28 randomly selected data points, demonstrated the reliability of the proposed rating curve equation, with percentage errors within an acceptable range of ±10%. This is particularly noteworthy given the inherent challenges in measuring discharge during flood conditions, where traditional methods often fall short. The research contributes to the field by presenting a practical and efficient method for estimating river discharge, especially in challenging environments such as the Varanasi bend of the River Ganga. The utilization of modern measurement technologies and the development of a reliable rating curve not only provide a valuable tool for researchers and hydrologists but also offer a means to enhance our understanding of river behaviour and improve flood prediction capabilities.

The authors followed the ethical guidelines and no ethical approval was required and all the authors agreed to participate.

All authors are agreeing to publish the content.

Funding information is not applicable/No funding was received.

M.S.C., P.K.S.D., and S.B.D. conceptualized the study and developed the methodology; M.S.C and P.J.O rendered support in formal analysis;; M.S.C, P.J.O. investigated the work; M.S.C. and P.J.O. wrote the original draft preparation; M.S.C., P.J.O., P.K.S.D., and S.B.D. wrote, reviewed, and edited the whole article.

The authors would like to express their sincere gratitude to the Department of Civil Engineering, IIT (BHU) Varanasi for providing the resources and support necessary to complete this research work. Padam Jee Omar gratefully acknowledges the support provided by UIET, Babasaheb Bhimrao Ambedkar University, Lucknow. The authors thank the reviewers for their constructive comments that helped improve the quality of this manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.